http://arxiv.org/abs/1003.3715
Spin and the Honeycomb Lattice: Lessons from Graphene
Matthew Mecklenburg, B. C. Regan
(Submitted on 19 Mar 2010)
Spin-1/2 particles such as the electron are described by the Dirac equation, which allows for two spin eigenvalues (up or down) and two types of energy eigenvalues (positive or negative, corresponding to the electron and the positron). A model of electrons hopping from carbon atom to carbon atom in graphene's honeycomb lattice gives low-energy electronic excitations that obey a relation formally identical to a two-dimensional Dirac equation. In graphene the spin equivalent, termed pseudospin, arises from the degeneracy introduced by the honeycomb lattice's two inequivalent atomic sites per unit cell. Previously it has been thought that the usual electron spin and the pseudospin indexing the graphene sublattice state are merely analogues. Here we show that the pseudospin is also a real, intrinsic angular momentum. This identification explains the suppression of electron backscattering in carbon nanotubes and the angular dependence of light absorption by graphene. Furthermore, it suggests that the half-integer spin of the quarks and leptons could derive from hidden substructure, not of the particles themselves, but rather of the space in which these particles live. In other words, the existence of spin might be interpreted as evidence that space consists of discrete points arranged in a non-cubic lattice.

How is what they are proposing any different from the Feynmann checkerboard model (also 2-d)?

As soon as I saw 2-d hopping reproducing Dirac, that is what pops to mind. And that doesn't require "two inequivalent atomic sites per unit cell".

Anyway, in answer to your question:
There are problems extending the checkboard models to 4-d spacetime. So that would have to be resolved confidently before people would start seriously considering curved spacetime and approaching a quantum gravity theory from this angle.